Theorem axc11rv 2139

Description: Version of axc11r 2187 with a disjoint variable condition on x and y, which is provable, on top of { ax-1 6-- ax-7 1935 }, from ax12v 2048 (contrary to axc11 2314 which seems to require the full ax-12 2047). (Contributed by BJ, 6-Jul-2021.) (Proof shortened by Wolf Lammen, 11-Oct-2021.)

Assertion

Ref	Expression
axc11rv	|- ( A. x x = y -> ( A. y ph -> A. x ph ) )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem axc11rv

Step	Hyp	Ref	Expression
1		axc16g 2134	. 2 |- ( A. x x = y -> ( ph -> A. x ph ) )
2	1	spsd 2057	1 |- ( A. x x = y -> ( A. y ph -> A. x ph ) )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  axc11vOLD  2141